Device for concentrating or collimating radiant energy

ABSTRACT

This invention consists in a nonimaging device for concentration or collimation of radiation on a receiver or from an emitter ( 14 ), depending on the case. The device is made up of the lens ( 50 ), which surrounds the receiver and consists of the aspheric surface ( 21 ), and the lens ( 15 ), whose upper refractive surface ( 16 ) may be aspheric, while the lower surface is aspheric ( 17 ) in its central portion (between points  18  and  19 ) and has a structure with discontinuous slope ( 20 ) in its external portion, in which the faces ( 22 ) fundamentally refract the rays while the faces ( 23 ) reflect them by total internal reflection. The design method provides that the device properties of concentration/collimation are noticeably superior to those of the existing inventions. Possible applications of this lens include: radiation sensors, illumination systems with LEDs, wireless optical communications and photovoltaic solar energy.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.10/148,736, which was filed on Oct. 15, 2002 and was a 35 U.S.C. 371National Stage of PCT/ES00/00459 of Dec. 1, 2000.

TECHNICAL FIELD

This invention relates to the field of optical systems; specifically,that of Nonimaging Optics.

BACKGROUND OF THE INVENTION

There exist previous inventions related to the present invention, allrelated to one another, for which various patents have been taken out(U.S. Pat. Nos. 4,337,759; 5,404,869; 5,577,493). While in a general waysome of the possible geometries of the present invention arequalitatively similar to those of these previous inventions, there areseveral fundamental differences that make this invention novel, and ruleout any conflict with the others. These differences lead to the opticalsurfaces of the invention being substantially different, due to the factthat the conditions imposed on their design are different, and thereforealso their resulting optical performance. In particular, the inventionpresented here can work very close (>95%) to the thermodynamic limit ofconcentration/collimation, while the previous inventions, not based onthe tools of Nonimaging Optics, are well short of this limit (<80%) whenthe angular spread of the ray bundles on passing through any of theoptical surfaces is large (>10 degrees).

The related patents are: the patent of Popovich et al. U.S. Pat. No.4,337,759, July/1982; that of W. A. Parkyn, Jr. et al., U.S. Pat. No.5,404,869, April/1995, and lastly, that of W. A. Parkyn, Jr. et al.,U.S. Pat. No. 5,577,493, November/1996.

The designs of all the mentioned inventions are not based (in contrastto this one) on the edge-ray theorem of Nonimaging Optics, so that theirfunctioning is limited with the extended bundles produced by manyemitters and receivers used in practice. U.S. Pat. No. 4,337,759,July/1982 and U.S. Pat. No. 5,404,869, April/1995 consider only thecentral ray of the bundles in the design. U.S. Pat. No. 5,577,493,November/1996 considers the so-called first-order optics around thecentral ray (Luneburg, 1964), which provides an order of approximationsuperior to the previously-mentioned device, but even so, theperformance attributed to it by its inventors for producing constantirradiance is only accurate for bundles with very small angular spread.

Furthermore, the invention protected by U.S. Pat. No. 5,577,493,November/1996 is axisymmetrical and considers as output bundle thatproduces uniform irradiance in 3D at the exit aperture. This bundle isonly a particular case of those considered in the present patent.

SUMMARY OF THE INVENTION

This invention includes a nonimaging concentration or collimation devicemade of two aspheric lenses, one of them containing a structure withdiscontinuous slope (i.e., faceted), that concentrates the radiationincident on a receiver or collimates the radiation from an emitter,depending on the case. The design method of this concentrator is basedon the nonimaging design method of Simultaneous Multiple Surfaces or SMS(Minano, Gonzalez, 1992).

For the design of this invention two extended (e.g., not punctual) raybundles are coupled in two-dimensional geometry (2D). The actualthree-dimensional (3D) devices are obtained by rotational symmetry(axisymmetrical) or translational symmetry (cylindrical), and theiroperation is analyzed a posteriori. Common examples of ray bundles(FIG. 1) are: (type 1) that composed of rays impinging on a segment (1)forming an angle inferior to a given angle (2) (called the acceptanceangle of the bundle) with the perpendicular to this segment, and (type2) that composed of the rays that intercept two given segments (3). Bothtypes of bundle can be defined in a more general way (type 3) if thesegments are substituted by arbitrary curves. FIG. 1 shows, in additionto two bundles of type 1 in FIG. 1(a) and type 2 in FIG. 1(b), a bundleof type 3, in FIG. 1(c) composed of the rays that intercept a rectangle(4) and a semicircumference (5) (this bundle is useful for modeling anLED or an IRED). Another bundle of rays (type 4) can be described, witha more general character than those of types 1 and 2 (which includesthem as particular cases), as that composed of the rays that impinge ona segment with an angle of incidence between two specified angles foreach point of the segment.

The design of the present invention is based on the so-called edge-raytheorem of Nonimaging Optics (Welford, Winston, 1989), which states thatto couple two bundles associated with the emitter and the receiver it isnecessary and sufficient to couple the subsets of edge rays of the two.The use of this theorem is the key to obtaining devices that work veryclose to the thermodynamic limit with bundles with wide angular spread.For example, the edge rays of the bundles in FIG. 1 are, for the type 1bundle, those that impinge on the segment with an angle of incidenceequal to the acceptance angle of the bundle and those that pass throughthe edges (6) and (7) of the segment; for the type 2 bundle, those thatpass through any of the edges (8), (9), (10) and (11) of the two givensegments; and for the type 3 bundle, those that are tangent to therectangle and those that pass through edges (12) and (13) of thesemicircumference.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1(a) illustrates a known type 1 bundle comprising rays that impingeon a segment (1) of edges (6) and (7) forming an angle inferior to theacceptance angle of the bundle (2) with the perpendicular to thatsegment.

FIG. 1(b) illustrates a known type 2 bundle comprising rays thatintercept two given segments (3). The edge rays of this bundle are thosepassing through any of the edges (8, 9, 10 and 11) of the two givensegments.

FIG. 1(c) illustrates a known type 3 bundle composed of the rays thatintercept a rectangle (4) and a semicircle (5) of edges (12) and (13).

FIG. 2 illustrates a basic working principle of the invention asconcentrator of radiation on a receiver (14). It comprises a lens (50)that surrounds the receiver comprising a refractive aspheric surface(21), and a second lens (15) whose upper side is a refractive asphericsurface (16) and whose lower side consists of another refractiveaspheric surface (17) in its central region (between points 18 and 19)and a discontinuous-slope structure (20) in its external region; whosefaces (22) fundamentally refract the rays and the faces (23) reflectthem by total internal reflection.

FIG. 3 illustrates a system of Cartesian coordinates (31) and initialgeometric parameters for carrying out the chosen design forconcentrating radiation on a receiver. The input bundle is defined bythe acceptance angle (24) and by the entry aperture defined by the edges(25) and (26) of the surface S₂. The output bundle is defined by thesegment of edges (27) and (51), which is the receiver and it isilluminated from surface S₃, whose edges are (29) and (30), with anangle of illumination limited to the acceptance angle (28).

FIGS. 4(a) and 4(b) illustrate teeth of the surface S₂ designed in thefirst phase for a device in accordance with the invention acting as aconcentrator as in FIG. 4(a) or as a collimator as in FIG. 4(b). As theyare of infinitesimal size (enlarged in the figure), the adjacent teethare identical, and the edge-ray bundles are parallel. It is desired thatthe light incident through segment (33), of edges (34) and (35), withslope between that of rays (36) and (37), is transmitted optimallythrough segment (38), of edges (39) and (40), with slope between that ofrays (41) and (42), which form angles (54) and (55) with the horizontalline, respectively. The geometry of the tooth with respect to itsmacroscopic tangent vector (32) is defined by the angles (56) and (57).

FIG. 5 illustrates a lens L₂ produced with two different dielectricmaterials separated by a spheric or aspheric refractive surface (43).

FIG. 6 illustrates a lens wherein surface S₁ can be substituted by adiscontinuous-slope Fresnel structure (44), which reduces weight andabsorption.

FIG. 7 illustrates a design of the surface S₁ as a discontinuous-slopestructure (45) with saw-toothed profile, which allows transmissionlosses to be minimized when the faces V do not coincide with flow lines(46) of the bundle transmitted by the continuous surface S₁.

FIG. 8 illustrates a lens wherein the central portion of S₂ can besubstituted by a discontinuous-slope Fresnel structure (47).

FIG. 9 illustrates a configuration wherein surfaces S₁ and S₂ of theprevious figures are interchanged, so that the teeth appear inverted(48).

FIG. 10 illustrates a device having an optically inactive portion (49)that joins the two lenses, and in such a way that they constitute asingle piece that includes an interior space (53).

FIG. 11 illustrates a device in accordance with the invention withaspheric faces (54) in an advanced mode, which allows them to be largerwhile maintaining excellent performance.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

A possible configuration of the invented device is that shown in FIG. 2,which also shows its basic working principle as a concentrator ofradiation on a receiver (14). The lens (15) L₁ has two active faces: theupper refractive surface (16), referred to as S₁, which is in generalaspheric, and the lower one, S₂, which consists of another refractiveaspheric surface (17) in its central portion (between points (18) and(19), which we shall call P and P′, respectively) and a structure withdiscontinuous slope (20) in its external portion. The lens (50) L₂surrounds the receiver and consists of the refractive aspheric surface(21), which we shall call S₃. The collected rays that impinge on thecentral portion (17) undergo three consecutive refractions beforereaching the receiver. On the other hand, the collected rays thatimpinge on the more external portion (20) undergo the followingincidences before reaching the receiver: a first refraction on thesurface S₁, a (possible) total internal reflection on the face (22)(which we shall call face V) of the teeth of S₂, a total internalreflection on the face (23) of those teeth (which we shall call face T),a second refraction on face V, and finally, a third refraction on S₃.The total internal reflection occurs when the angle of incidence of theray with the normal to the surface is greater than the so-calledcritical angle of the interface, which is given by sin⁻¹(1/n), n beingthe refractive index of the lens L₁.

Particular cases are those in which the profile of S₁ is circular orflat. The latter case is of especial interest in certain applications,such as photovoltaic concentration, since it permits the grouping of aset of devices fixed to a dielectric plate, such as a flat piece ofglass, which acts as a reference to provide parallelism between thedevices, as protection against the elements and as a filter forultraviolet radiation.

In the design the surfaces S₂ and S₃ are calculated from thespecification of the profile of the surface S₁ and of the input andoutput bundles. The definition of the input bundle can be made beforeits refraction on S₁, so that its definition would be independent ofthat of that surface. For example, it could be a type 1 bundle withacceptance α and with the edges of the segment coincident with theextreme points of the surface S₁. Another possibility, which could beinteresting in practice, is that of defining the input bundle after itsrefraction on S₁, which allows, for example, the segment crossed by therays of the bundle to be that defined by the two extreme points of thesurface S₂. This implies that the specifications of the bundle and ofthe surface are interdependent: if we wish to define the bundle as thatcomposed of the rays that impinge within the acceptance α before therefraction on S₁ and with the edges of the segment coincident with thetwo extreme points of the surface S₂, it will be necessary, in general,to carry out a ray-tracing on the surface S₁. In the case that thesurface S₁ is flat, this ray-tracing is unnecessary, since therefraction in this dioptric is trivial, and the specification of thebundle after the refraction is therefore immediate by application ofSnell's Law: it will be a type 1 bundle with acceptance angle equal toα′=sin⁻¹(1/n sin α), n being the refractive index of the lens L₁.

In order to simplify the explanation, and by way of an example, let ussuppose that S₁ is a plane, that the input and output bundles are bothtype 1, and that the two bundles are symmetrical with respect to anaxis, as FIG. 3 shows. For the other types of bundle the procedure isanalogous. The input bundle (specified after the refraction on S₁) isdefined by the acceptance angle (24) with value α′, and by the edges(25) and (26) of the surface S₂, which we shall call I and I′, and whichdetermine the segment we shall refer to as the entry aperture. Theoutput bundle is defined by the receiver, which is the segment of edges(27) and (51), called respectively R and R′, and by the angle ofillumination limited to the acceptance angle (28) of value β (the normalconsideration when the sensitivity of the receiver is low for verygrazing angles, as is common in photodiodes or solar cells). The edges Oand O′ of the surface S₃ are the symmetrical points (29) and (30). Thisfigure also shows the system of Cartesian coordinates (31) that will beused for the description, and whose origin is centered on the receiver.

Input design parameters (apart from the profile of the surface S₁) arethe angles α and β, the distance RR′, the refractive index of thedielectric materials to be used (n for the lens L₁ and n′ for L₂), theordinate of point I, the abscissa of point O and the abscissa of pointP. The ordinate of point O is calculated immediately from its abscissa,the distance RR′ and the angle β. However, the calculation of theabscissa of point I and of the ordinate of point P will be obtainedlater, as the result of the design.

The design procedure consists of three phases. In the first phase thedesign conditions for the teeth of the surface S₂ (which will bedifferent for concentration and collimation) are chosen, supposing thatthey are of infinitesimal size. With these conditions the calculation ismade of the expressions that constitute the individual design of teethfor the different angles of incidence with respect to the mean normalvector of the tooth. Designed simultaneously in the second phase, withthe SMS method, are the surfaces S₂ and S₃ that couple the output andinput bundles, taking into account the expressions calculated in thefirst phase. Lastly, in the third phase, the teeth of the surface S₂ aregenerated with finite size (as manufactured in practice) on the basis ofthe infinitesimal teeth calculated in the previous phase.

There are different possible design modes, according to the level ofcomplexity of the finite-size teeth of the surface S₂ both in theirdesign in the third phase and in their manufacture. Thus, we can defineas basic mode that in which the profiles of the T faces are rectilinear,as standard mode that in which these profiles are arcs of circumference,and as advanced mode that in which they are aspheric. The three modesconverge on one another when the size of the teeth is very small(providing an operating quality coincident with that predicted forinfinitesimal teeth), but their performance degrades differently whenthe size of the teeth is greater. In increasing order of quality are thebasic, standard, and advanced modes. Since the design of the standardand advanced modes is carried out from the basic mode, we shall begin bydescribing this before proceeding with the explanation of the others.

Let us consider for the first phase the description of a tooth designedin the first quadrant operating as a concentrator as shown in FIG. 4(a).Given that the size of the tooth is infinitesimal (enlarged in thefigure), this means that, in the scale of the figure, adjacent teeth areidentical, and that the wavefronts associated with the edge rays areflat. The vector (32), which we shall call t, is the macroscopic tangentvector of the surface S₂. It is desired that the light incident throughsegment (33), of edges (34) and (35), with slope between that of rays(36) and (37), which we shall call, respectively, e(+) and e(−), istransmitted optimally through segment (38), of edges (39) and (40), withslope between that of rays (41) and (42), which we shall call,respectively, i(−) and i(+). To this end the following designcharacteristics will be imposed: (1) that no undesired incidences occur,and (2) that the irradiance on leaving the tooth is as uniform aspossible. Both characteristics are obtained on demanding the twofollowing conditions. On the one hand, that face V (also identified asface 22 of FIG. 2) is parallel to the bisector of the impinging bundle,which coincides with the so-called flow line of the bundle (Welford,Winston, 1989). Face V situated in this way has the property ofreflecting (through total internal reflection) the bundle without itsgeometry being modified. On the other hand, it should be demanded thatthe ray e(−) that impinges at point (34), after the total internalreflection on face T and the refraction on face V, is transformed intothe ray i(−) that passes through point (40). Note that rays i(−)transformed from rays e(−) pass through all the points of segment (38),but that rays i(+) emerge from only a portion of segment (38) (for thisreason the irradiance is not uniform in (38), though it as uniform aspossible, as required by condition (2)). Nevertheless, in the secondphase the rays i(+) and i(−) will be used as though they emerged fromthe whole of segment (38), which means that it will not be possible toreach the thermodynamic limit of concentration/collimation (although theinvention comes very close to doing so).

These two conditions for the design of the infinitesimal teeth, whichguarantee their optimum functioning, constitute another innovation withrespect to the above-mentioned related patents, none of which includesthese conditions.

FIG. 4(b) shows a tooth for the basic design operating as a collimator.As it can be seen, the difference with respect to the case of FIG. 4(a),in which it was designed as a concentrator, lies in the second imposedcondition: in this case it is the ray e(+) that impinges at (34) thatmust be transformed into the ray i(+) that passes through point (40).

On imposing the two mentioned conditions it is deduced that face V isvertical, and the following expressions relating the angles involved areobtained by trigonometric calculations:(a) tan δ=tan ψ+(sin ψ)(n ²−sin² ψ)⁻²+tan γ  (Eq. 1.a)(b) n cos(2δ−α′)+sin φ=0  (Eq. 1.b)(c) n cos(2δ+α′)+sin φ′=0  (Eq. 1.c)

where φ, φ′, δ and γ are, respectively, the angles (54), (55), (56) and(57) shown in FIGS. 4(a) and 4(b), n is the refractive index of the lensand ψ≡φ in the design of the concentrator and ψ≡φ′ in that of thecollimator.

In the second phase, in which the profiles of the surfaces S₁ and S₂ aredesigned, the following steps are observed:

-   -   a) Select a value for the abscissa of point I (this value will        be recalculated later).    -   b) Through the (inverse) application of Snell's Law, calculate        the vector tangent to S₃ at point O with the condition that the        ray that impinges from I must be refracted at O toward R.    -   c) Calculate the angle δ of the infinitesimal tooth situated at        point I with the condition that the ray i(+) associated with the        tooth is directed toward O. This can be achieved using the        equation (Eq. 1.c), where the angle φ′ is calculated from the        points I and O. Calculate also the angle φ using (Eq. 1.b), the        angle γ using (Eq. 1.a), and from this, calculate t_(I)=(−cos γ,        sin γ), which is the macroscopic vector tangent to S₂ at I.    -   d) Find the first section of S₃ above O with the condition that        the rays proceeding from I are refracted on that portion toward        the receiver with angle of incidence β. The solution to this        problem is given by the constancy of optical path from point I        up to a flat wavefront sloped with the angle β, and is an        ellipse. This constitutes a particular case of the so-called        Cartesian ovals. The tangent to S₃ at these points can be found,        once these have been calculated, by (inverse) application of        Snell's Law as in step a). The last point of this portion is        marked by the ray that, after refraction, passes through R′.    -   e) Find the following section of S₃ with the condition that the        rays proceeding from I are refracted on that portion toward        point R′. Once again, the solution is given by the constancy of        optical path between the two points, and constitutes a        particular case of Cartesian ovals, and the tangent to S₃ at        these points is found by (inverse) application of Snell's Law.        The last point of this section, which will be called H₀ and its        tangent t_(H0), is that for whose calculation the ray i(−) that        comes from I has been used.    -   f) Rename I, t_(I), O and to as F₀, t_(F0), G₀ and t_(G0),        respectively. From the sections of S₃ calculated in d) and f)        select a number M of uniformly-distributed points (for example,        M=500) and name them from F₁ to F_(M), with tangents t_(F1) to        t_(FM). Note that H₀≡F_(M) (y t_(H0)≡t_(FM)).    -   g) Find the following macroscopic point G₁ of the surface S₂ as        the point of intersection between the straight line that passes        through G₀ with direction vector t_(G0) and the trajectory of        the ray refracted at F₁ proceeding from R (traced in the reverse        direction). This ray is the ray i(+) associated with the        infinitesimal tooth at G₁, so that it also gives the angle φ′ at        that point. With equations (Eq. 1.c), (Eq. 1.b) and (Eq. 1.a) we        can calculate, respectively, the angles δ, φ and γ, and from the        last of these, t_(G1)=(−cos γ, sin γ), which is the macroscopic        vector tangent to S₂ at G₁.    -   h) Calculate the following point H₁ of the surface S₃ as the        point of intersection between the straight line that passes        through H₀ with direction vector t_(H0) and the ray i(−)        associated with the infinitesimal tooth of G₁. The tangent        t_(H1) to S₃ at H₁ can once more be found by (inverse)        application of Snell's Law. Identify H₁≡F_(M+1) (and        t_(H1)=t_(FM+1)).    -   i) Repeat steps g) and h), increasing the subindices by one        unit, until the abscissa of a point G_(n) is greater than the        abscissa of point P (selected as entry parameter). Since the        precision on the abscissa of point P chosen is not important        (and that, this precision being determined by the value of the        chosen parameter M in step f), it can be improved through        choice), it will be considered for what follows that P≡G_(n).

The profile of the central region of S₂ (between P and P′) will becalculated (together with the remaining portion of S₃), once againaccording to the edge-ray theorem, so that it directs the rays e(+)toward R′ and the rays e(−) toward R (note that this assignation is theopposite of what was carried out in steps g) and h) for the exteriorportion of S₂). Given that the surfaces are continuous, this impliesthat the optical path from the wavefront associated with rays e(+) up toR′ will be constant, as will that from the wavefront associated withrays e(−) up to R. So that the surfaces S₂ and S₃ do not havediscontinuities in their respective vertices, the symmetry of the designobliges the two optical paths (measured with respect to symmetricalwavefronts), moreover, to be equal. This condition will allow evaluationof the initial choice of the abscissa of point I.

-   -   j) Find the tangent to S₂ at P so that the impinging ray e(−) is        transformed after refraction into the ray i(+) calculated at        point P in step i). Calculate the ray e(+) after the refraction        at P. If the angle it forms with the horizontal is superior to        the angle φ calculated at point P in step i), return to the        beginning choosing a lower value for the abscissa of point P.    -   k) Calculate a new section of S₃ next to point H_(n) found in        step i) with the condition that the rays coming from P are        refracted on that portion toward point R′. Once again, the        solution is given by the constancy of optical path between the        two points, and the tangent to S₃ at these points is found by        (inverse) application of Snell's Law. The last point of this        section is that for whose calculation the ray e(+) after        refraction at P has been used. Choose a number M′ of        uniformly-distributed points (for example, M′=50) and name them        in a way correlative to the previous ones, that is, from H_(n+1)        to H_(n+M′) (and from F_(M+n+1) to F_(M+n+M′)).    -   l) Calculate the optical paths C(+) and C(−) associated with the        rays e(+) up to R′ and the rays e(−) up to R, respectively.    -   m) Repeat the steps from a) to l) iterating on the value of the        abscissa of point I until it is achieved that |1−C(+)/C(−)|<ε,        with ε being a pre-fixed margin of error (e.g., 0.0001).    -   n) Calculate the following point G_(n+1) of S₂ with the        condition that the trajectory of the ray refracted at F_(n+1)        coming from R (traced in the reverse direction) is transformed        after refraction at the desired point into a ray e(−). Once        again, the solution is calculated because the optical path C(−)        is known, and the tangent to S₂ at G_(n+1) is found by (inverse)        application of Snell's Law.    -   o) Calculate the following point H_(n+M′+1) of S₃ with the        condition that the trajectory of the ray e(+) refracted at        G_(n+1) is directed, after refraction at the desired point        toward R′. Again, the solution is calculated because the optical        path C(+) is known, and the tangent to S₃ at H_(n+M′+1) is found        by (inverse) application of Snell's Law.    -   p) Repeat steps n) and o) until the symmetry axis is reached,        that is, until the abscissas of points G and H calculated are        negative.

Finally, to conclude the basic design there remains only the thirdphase, which involves the generation of the teeth of S₂ with finite size(as they will be manufactured in practice) and faces with rectilinearprofile on the basis of the macroscopic surface and the infinitesimalteeth calculated in the previous phase. The procedure moves from theedge toward the center of the lens observing the following steps:

-   -   a) Select, for example, size D of the horizontal projection of        the finite teeth. This size should be such that that the        subsequent ray-tracing shows no important degradation in the        functioning of the device with respect to that obtained with        size D/2.    -   b) Take as central points of the finite teeth those points G_(i)        of the macroscopic surface between P and I whose abscissa differ        less from point I by an odd number of times D/2.    -   c) Define the slope of the face T of the finite tooth to which        G_(i) belongs as the slope of the face T defined at G_(i) by the        infinitesimal tooth. The face T of the finite tooth is extended        symmetrically with respect to the point.    -   d) The faces V are thus situated at abscissas that differ from        point I by a whole number of times D.

The basic concentrator design is complete. In this last phase anothercriterion can be taken for the generation of finite teeth, such as thatthe distance between the upper and lower evolvent of the teeth takes thevalue D. The generation procedure is similar to that described, and theadjustment of the central points G_(i) of each tooth can carried out inan iterative way.

The standard mode differs from the basic mode in the third phase, wherethe faces T of the finite teeth have an arc of circumference as aprofile. The design procedure of this mode is similar to that of thebasic one. In the second phase, although the resulting design isidentical, the standard mode adds the calculation of the curvature ofthe faces T of the infinitesimal teeth (for its later use in the thirdphase), which constitutes a higher order of precision than that employedin the basic mode. In order to make this calculation the followingequation is used, which relates the radii of curvature of a surface andthose of the incident and refracted/reflected wavefronts:(n _(i) cos² θ_(i))/ρ_(i)+(n _(r) cos² θ_(r))/ρ_(r)=(n _(i) cos θ_(i) −n_(r) cos θ_(r))/ρ_(s)  (Ec. 2)

where the sub indices i, r and s refer to the incident wavefronts,refracted/reflected wavefronts and the surface, respectively, n denotesthe refractive index, θ the angle of the ray with respect to the normaland ρ the radius of curvature. Equation (Eq. 2) is applied to thereflection, making θ_(r)=θ_(i) and n_(r)=n_(i).

In order to calculate the radius of curvature ρ_(sT) of the face T ofthe infinitesimal teeth it is necessary to find first the radius ofcurvature of S₃ at points F₁ to F_(M) during their calculation in stepsd) and e) of the second phase. For this the expression (Eq. 2) isapplied to the refraction at these points of the rays coming from I. Inthis case, for each point F_(k) and denoting by AB the length of thesegment of edges A and B, we have ρ_(i)= (IF_(k)), ρ_(r)=∞ in step d)and ρ_(r)= R′F_(k) in step e).

It is in step f), in which the points G_(k) are calculated on the basisof the points F_(k), where the desired values of ρ_(sT) should becalculated. The calculation involves the use of the expression (Eq. 2)for the three successive incidences undergone by the ray that goes (inthe reverse direction) from R toward F_(k). Given that in step f) thepoints and the normals to the surfaces are calculated, the angles ofincidence and of refraction/reflection, like the refractive indices, areknown parameters in the three incidences. In the first, at F_(k), as theradius of curvature ρ_(s) is already known and ρ_(i)= RF_(K) , from (Eq.2) we obtain the radius of curvature of the refracted wavefront ρ_(r1).For the second incidence, which occurs on the face V of the toothcalculated at G_(k), the radius of curvature of the incident wavefrontis ρ_(i)= G_(k)F_(k) −ρ_(i) and the radius of curvature of the surfaceis known (ρ_(sv)=∞), so that from (Eq. 2) we obtain the radius ofcurvature of the refracted wavefront ρ_(r2). Finally, for the thirdincidence, which occurs on the face T of the tooth, it is known thatρ_(i)=ρ_(r2) and ρ_(r3)=∞, so that (Eq. 2) can be solved with the radiusof curvature ρ_(sT) as an unknown, which was the desired value.

Given that in step g) new points F_(j), are calculated, initially calledH_(k), and which will be used again in step f) on repeating it as h)indicates, it is also necessary to calculate the radius of curvature ofS₃ at these points. For this, the procedure is analogous to that of thecalculation of ρ_(sT) previously indicated, using the trajectory of theray used to calculate H_(k), which is the ray e(+) impinging at G_(k),and taking advantage of the fact that ρ_(sT) is already known.

The third phase of the standard mode, which concerns the generation ofthe teeth of finite size, differs from the basic mode in that the Tfaces, instead of being rectilinear, are generated as arcs ofcircumference. The procedure of generating the teeth is analogous tothat seen for the basic mode, the only difference being that the face Tof the finite tooth to which the central point G_(i) of a finite toothbelongs is the arc of circumference that passes through that point, withthe slope and radius of curvature associated with the infinitesimaltooth, and that extends symmetrically with respect to the point. Thisconcludes the standard design mode.

Lastly, the advanced design mode is characterized by the faces T of theteeth having an aspheric profile. The calculation of these profiles ismade from the finished basic design (with finite teeth), observing thefollowing steps:

-   -   a) Trace in the reverse direction the uniparametric ray bundles        that leave from R and R′ and are refracted on S₃ and on the        faces V of the finite teeth.    -   b) For each tooth, whose central point is G_(i), calculate the        aspheric profile of the face T that passes through G_(i) and        whose points Q are such that the ray that impinges vertically is        reflected in accordance with the direction bisecting of the rays        of the uniparametric bundles that pass through Q calculated in        a). This problem, which can be expressed in the form of a        first-order differential equation, has a single solution when        one ray—and only one of each bundle—passes through each point Q.

The advanced design mode is finished. FIG. 11 shows an example of anadvanced design. As mentioned above, the provision of aspheric profiles(54) for the facets allows them to be made larger than in the basic andstandard modes while maintaining excellent performance, even close tothe thermodynamic limit.

The description of the design procedures for the three modes (basic,standard and advanced) is finished.

The design is essentially similar in the case that the profiles of thefaces V are not vertical lines, but have a pre-fixed slopingrectilinear, circular or aspheric profile. In fact, an aspect notconsidered in the descriptions of the designs concerns the fact that themanufacture of teeth with totally vertical faces V may be impractical(in the case of lens manufacture by plastic injection, removal of thepart from the mould is difficult). It is possible to correct thisaspect, for example, by considering design of the faces V withinclinations of a certain angle (in the range of 0.5 degree to 1 degreemay be sufficient), which entails appropriate modification of theequations (Eq. 1). This inclination is also useful to avoid theundesired effects produced in practice by the rounding of the verticesof the teeth. As a negative consequence, a sloping face V means that itis not parallel to a flow line of the incident bundle, so that thereflection on that face will modify (slightly) the geometry of thebundle. This means that the characteristic of angular transmission willbe degraded (i.e., it will be less stepped) with respect to thatcorresponding to vertical faces V. Meanwhile, the profiles of the facesV can be produced as arcs of circumference or pre-fixed aspheric curvesto facilitate their manufacture even more (at the cost of making theproduction of the mould more difficult), by decreasing, for example, thecurvature necessary for the profiles of the faces T.

Another aspect not dealt with up to now concerns the fact that thecondition imposed on the design of the infinitesimal teeth inconcentration that obliges the edge ray e(−) impinging at point (34) tobe transformed into the ray i(−) that passes through point (40) may berelaxed (i.e., allowing it to pass slightly above or below that point)without producing a serious degradation in functioning.

Taking into account all of these considerations, we can affirm theusefulness of the possibility of the profiles of the faces V or T havingat each point a slope modified by an angle of less than 2 degrees.

The device described for concentrating radiation on a receiver may beaxisymmetrical or cylindrical, and is characterized by transforming theedge rays of an input extended ray bundle into edge rays of an outputextended ray bundle that illuminates a receiver, both bundles beingdefined in the plane of a cross-section (which contains the symmetryaxis in the axisymmetrical case, or is perpendicular to the direction ofsymmetry in the cylindrical case), by means of: (a) a lens L₁ composedon one side of a refractive aspheric surface, S₁, on which the inputbundle impinges, and on the other side, S₂, of another refractiveaspheric surface in its central region and with a discontinuous-slopestructure in its external region, whose cross-section is formed of teethwith two aspheric faces such that one of them, V, is parallel to theflow lines of the bundle transmitted by the dioptric S₁, and the otherface, T, reflects the bundle by total internal reflection toward theface V where it is refracted so that no ray intercepts the adjacenttooth and that the nearest edge ray to do so is tangent to that tooth;and (b) a second lens L₂ that surrounds the receiver composed of anrefractive aspheric surface on which the bundle transmitted by the lensL₁ impinges.

On the other hand, the device used for collimating the radiationgenerated by an emitter may be axisymmetrical or cylindrical, and ischaracterized by transforming the edge rays of an input extended raybundle generated by an emitter into edge rays of an output extended raybundle, both bundles being defined in the plane of a cross section, bymeans of: (a) a lens L₂ that surrounds the emitter composed of arefractive aspheric surface on which the input bundle impinges; and (b)a second lens L₁ composed on one side of a refractive aspheric surface,S₁, from which the output bundle leaves, and on the other side, S₂, ofanother refractive aspheric surface in its central region and with adiscontinuous-slope structure in its external region, whosecross-section is formed of teeth with two aspheric faces such that onone of them, V, the bundle transmitted by the dioptric S₃ is refractedso that all the rays are reflected by total internal reflection on theother face, T, that the edge ray nearest to not being reflected istangent to the profile of the tooth, and that the face V is parallel tothe flow lines of the bundle transmitted toward S₁.

U.S. Pat. No. 5,577,493, November/1996 describes an axisymmetric devicewhich is qualitatively similar to this invention, and it is used tocollimate the radiation generated by an emitter and in which the bundlesof rays are chosen to provide uniform irradiance in three dimensions atthe exit aperture. However, due to the restrictions of that designmethod, the device disclosed will provide such performance only when theangular spread of the ray bundles on passing through any of the opticalsurfaces is small (<10 degrees). Moreover, the design conditions of theinfinitesimal teeth used in this invention (Equations 1.a, 1.b, and1.c), which guarantee the optimal performance of the teeth, are not usedin the '493 patent, which leads to the optical surfaces of theirinvention being substantially different and their resulting opticalperformance being noticeably inferior.

The procedures described for the three design modes are equallyapplicable to the situation shown in FIG. 5, in which the lens L₂consists of two different dielectric materials separated by a sphericalor aspheric refractive surface (43), with pre-fixed profile, justconsidering the refraction of the edge rays on this surface during theprocess.

A variant of the configuration described up to now consists insubstituting the refractive surface S₁ by a discontinuous-slope Fresnelstructure (44), as shown for example in FIG. 6 for the case of the flatand horizontal S₁. It is thus possible to use less dielectric material,which reduces its weight and absorption. The two surfaces, discontinuousand continuous, work in the same way. In fact, the profiles of theremaining optical surfaces are identical in the two designs. The onlydifference with respect to the trajectories of the rays is that thesecan now impinge on the vertical face of the steps, the face thatcoincides with the flow lines of the incident bundle. This implies, onceagain, that if these faces were mirrors the reflection of the rays onthem would not modify the geometry of the transmitted bundle. Althoughwhen the incidence takes place from the interior face of the dielectricmaterial this interface indeed behaves like a mirror due to thephenomenon of total internal reflection, this is not the case withincidence from the air, which leads to some losses. Nevertheless, forsmall acceptance angles α(<5°) these losses are negligible due to thecombination of two effects: the reflectivity of this interface, althoughnot 100%, is very high for large angles of incidence (and in the presentcase they will be superior to 90°−α), and the fraction of rays thatimpinge on the vertical faces from the air is also small if theacceptance angle is moderate.

The surface S₁ as a discontinuous-slope structure can also have anotheruse, as FIG. 7 shows. In this case the flat dioptric of FIG. 2 has beensubstituted by a discontinuous-slope structure with saw-toothed profile(45) that diverts the input bundle to modify the direction of the flowlines (46). The lens is attached to a dielectric plate 45′ by means ofan adhesive 45″ with a refractive index slightly different from that ofthe lens. This structure refracts the rays of the incident bundle sothat they progress toward S₂ with a slight divergent direction. Thismeans that the face V of the teeth of the external region of S₂, ifdesigned with a non-null tilt angle to facilitate manufacture, willproduce a lesser degradation of the optical performance on being closerto (or even coinciding with) the divergent flow line. As the verticalface of the S₁ in turn causes a degradation (by blocking the raytrajectories), for each inclination of the faces V there is an optimumangle of divergence of the bundle, for which degradation is minimum.

Another possibility (which can also be combined with any of the previousones) consists in making the central portion of S₂ as adiscontinuous-slope Fresnel structure (47), as shown in FIG. 8.

Another possible configuration consists in designing the lens with thesurfaces S₁ and S₂ interchanged, so that the teeth appear inverted (48),as shown in FIG. 9. In the case of rotation symmetry, for its productionby molding, it is necessary for either the mould or the lens to beflexible, so that the lens can be extracted from the mould. In the caseof translation symmetry this would be unnecessary, since manufacturecould be by extrusion. The design procedure of the optical surfaces iscommon to all the configurations indicated.

In the proposed invention, used for concentrating radiation on areceiver, this could be optoelectronic, such as a photodiode,phototransistor or solar cell. On the other hand, if it is used forcollimating the radiation produced by an emitter, this could also beoptoelectronic, such as an LED, an IRED or a laser.

The manufacturing of the concentrator of this invention can be carriedout using a diamond-tip lathe with numerical control (CNC) on plasticmaterial, such as acrylic (PMMA). Another possibility worthy of mentionis that of the injection of the PMMA in a suitable mould, which allows aproduction also covered by this application, and which is shown in FIG.10: the device can be manufactured with an optically inactive portion(49) that joins the two lenses, and in such a way that they constitute asingle piece that includes an interior space (53). The joining can becarried out by contact before solidification of the final injected partor by means of subsequent gluing. As it is a single piece, the spacebetween the lenses is protected from dust and humidity. This space canbe evacuated or filled, if desired, with an inert gas. The adhesion ofthe receiver or the emitter to the secondary can be carried out by meansof the casting of a transparent epoxy resin.

The improvements and differences this invention introduces with respectto the mentioned state of the art can be summarized as follows:

-   -   (a) The designed surfaces and the faces of the teeth are such        that the device couples in two dimensions the edge rays of two        extended ray bundles, while those of the mentioned inventions        couple only the central ray of the bundles or its first-order        environment.    -   (b) In the case of the axisymmetric device to collimate the        radiation generated by an emitter, the design ray bundles        include as a particular case the one that produces uniform        irradiance in the exit aperture, the case considered in U.S.        Pat. No. 5,577,493, November, 1996, but in said patent the        design that is described there is only adequate when the angular        spread of the ray bundles on passing through all of the optical        surfaces is small (<10°).    -   (c) The conditions for the design of the infinitesimal teeth        facets used in this invention (given by the Equations 1.a, 1.b,        & 1.c, which provide that the faces of the teeth are such that        one guides the bundle as a flow line, they produce maximum        uniformity of irradiance at the exit of the tooth, and they        avoid undesired incidence on the adjacent tooth) are not used in        the previous state of the art, which lead to the optical        surfaces of the invention being substantially different, and        also their resulting optical performance.    -   (d) Its use as a concentrator on a receiver.    -   (e) The cylindrical symmetry, where appropriate.    -   (f) Its possible manufacture as a single part with an interior        space.    -   (g) The grouping of a set of devices fixed to a dielectric        plate.

Differences (a) and (c) confer upon this invention an opticalperformance noticeably superior to that of the previous inventions,especially when the angular spread of the ray bundles as they passthrough any of the optical surfaces is large (>10 degrees).

The presented invention has direct applications in diverse fields, suchas that of radiation sensors, illumination systems with LEDs, wirelessoptical communications or photovoltaic solar energy.

In the field of sensors, the proposed invention allows the achievementof high sensitivities, close to the thermodynamic limit, withoutaffecting the simplicity and compactness of the device. Also, in thefield of illumination with LED, this invention provides anoptimally-collimated bundle with geometry readily compatible withcurrent production techniques.

In wireless optical communications, the control of angular response ofthe emitting and receiving devices and the use of almost all possibledirections of emission/reception in the design permits connections whosesignal-noise relationship is close to the maximum possible. Employed inreception, the proposed invention would use an optoelectronic sensor asreceiver (e.g., a photodiode or phototransistor); in transmission theinvention would use an optoelectronic emitter (LED, IRED or laser).

Finally, in photovoltaic applications this invention constitutes anappropriate device for high-concentration solar cells. Its performanceclose to the theoretical limit means that for a given concentrationfactor, the angular acceptance of the device is close to the maximumpossible, which is useful for permitting high tolerances in themanufacture of the device itself and in the alignment of several of themto form a module (which can be made simply by gluing them to a flatpiece of glass), a light support structure for modules with lowsun-tracking accuracy.

1. Device for concentrating radiant energy wherein said device isaxisymmetrical or cylindrical and is configured to transform the edgerays of an input extended ray bundle into edge rays of an outputextended ray bundle that illuminates a receiver, the optical spread ofsaid input and output bundles being greater than ten degrees at one ormore of the optical surfaces of said device and said bundles beingdefined in the plane of a cross-section by: a) a lens L₁ comprising onone side a refractive aspheric surface, S₁, on which the input bundleimpinges, and on the other side, S₂, another refractive aspheric surfacein its central region and a discontinuous-slope structure in itsexternal region, said discontinuous-slope structure cross-sectioncomprising teeth with two aspheric faces such that one of them, V, isconfigured to be parallel to the flow lines of the bundle transmitted bysaid surface S₁, and the other face, T, is configured to reflect thebundle by total internal reflection toward the face V where it isrefracted so that no ray intercepts the adjacent tooth and that thenearest edge ray to do so is tangent to that tooth, and b) A second lensL₂ that surrounds the receiver composed of a refractive aspheric surfaceon which the bundle transmitted by the lens L₁ impinges.
 2. Device forconcentrating radiant energy according to claim 1 wherein said receivercomprises an optoelectronic receiver.
 3. Device for concentratingradiant energy according to claim 1 wherein said receiver is one of aphotodiode, a phototransistor or a photovoltaic cell.
 4. Device forconcentrating radiant energy according to claim 1 wherein the profilesof the faces of the teeth have at each point a slope modified by anangle of less than 2 degrees.
 5. Device for concentrating radiant energyaccording to claim 1 wherein the profile of S₁ is circular or flat. 6.Device for concentrating radiant energy according to claim 1 wherein thesurfaces S₁ and S₂ of the lens are interchanged, so that the teethappear inverted.
 7. Device for concentrating radiant energy according toclaim 1 wherein S₁ has a saw-toothed profile that diverts the inputbundle to modify the direction of the flow lines.
 8. Device forconcentrating radiant energy according to claim 1 wherein S₁ or therefractive surface of the central portion of S₂, or both, arediscontinuous-slope Fresnel structures.
 9. Device for concentratingradiant energy according to claim 1 wherein the lens L₂ comprises twodifferent dielectric materials separated by a spheric or asphericrefractive surface.
 10. Device for concentrating radiant energyaccording to claim 1 wherein the cross-sections of the teeth of S₂ havefaces with circular or rectilinear profiles.
 11. Device forconcentrating radiant energy according to claim 1 comprising anoptically inactive portion joining the two lenses so that theyconstitute a single part that includes an interior space.
 12. Device forconcentrating radiant energy according to claim 1 fixed to a dielectricplate.
 13. Device according to claim 1 wherein at least one of saidsurfaces S₁, S₂, or S₃ comprises a Cartesian oval.
 14. Device forcollimating radiant energy wherein said device is axisymmetrical orcylindrical and is configured to transform the edge rays of an inputextended ray bundle generated by an emitter into edge rays of an outputextended ray bundle, the optical spread of said input and output bundlesbeing greater than ten degrees at one or more of the optical surfaces ofsaid device, both of said bundles being defined in the plane of across-section, by: a) a lens L₂ that surrounds the emitter and comprisesa refractive aspheric surface S₃ on which the input bundle impinges, andb) a second lens L₁ comprising on one side a refractive asphericsurface, S₁, from which the output bundle leaves, and on the other side,S₂, another refractive aspheric surface in its central region and adiscontinuous-slope structure in its external region, saiddiscontinuous-slope structure cross-section comprising teeth with twoaspheric faces such that on one of them, V, the bundle transmitted bysaid surface S₃ is refracted so that all the rays are reflected by totalinternal reflection on the other face, T, that the edge ray nearest tonot being reflected is tangent to the profile of the tooth, and that theface V is parallel to the flow lines of the bundle transmitted towardS₁.
 15. Device for collimating radiant energy according to claim 14wherein said emitter comprises an optoelectronic emitter.
 16. Device forcollimating radiant energy according to claim 14 wherein said emitter isone of an LED, an IRED or a laser.
 17. Device for collimating radiantenergy according to claim 14 wherein the profiles of the faces of theteeth have at each point a slope modified by an angle of less than 2degrees.
 18. Device for collimating radiant energy according to claim 14wherein the profile of S₁ is circular or flat.
 19. Device forcollimating radiant energy according to claim 14 wherein the surfaces S₁and S₂ of the lens are interchanged, so that the teeth appear inverted.20. Device for collimating radiant energy according to claim 14 whereinS₁ has a saw-toothed profile that diverts the input bundle to modify thedirection of the flow lines.
 21. Device for collimating radiant energyaccording to claim 14 wherein S₁ or the refractive surface of thecentral portion of S₂, or both, are discontinuous-slope Fresnelstructures.
 22. Device for collimating radiant energy according to claim14 wherein the lens L₂ comprises two different dielectric materialsseparated by a spheric or aspheric refractive surface.
 23. Device forcollimating radiant energy according to claim 14 wherein thecross-sections of the teeth of S₂ have faces with circular orrectilinear profiles.
 24. Device for collimating radiant energyaccording to claim 14 comprising an optically inactive portion joiningthe two lenses so that they constitute a single part that includes aninterior space.
 25. Device for collimating radiant energy according toclaim 14 fixed to a dielectric plate.
 26. Device according to claim 14wherein at least one of said surfaces S₁, S₂, or S₃ comprises aCartesian oval.
 27. Device for collimating radiant energy, said devicebeing axisymmetrical or cylindrical and configured to transform the edgerays of an input extended ray bundle generated by an emitter into edgerays of an output extended ray bundle, both bundles being defined in theplane of a cross-section, excluding the axisymmetric case in which thebundles of rays are chosen to provide uniform irradiance in threedimensions at the exit aperture when the angular spread of the raybundles on passing through all of the optical surfaces is smaller than10°, by: a) a lens L₂ that surrounds the emitter comprising a refractiveaspheric surface S₃ on which the input bundle impinges, and b) a secondlens L₁ comprising on one side a refractive aspheric surface, S₁, fromwhich the output bundle leaves, and on the other side, S₂, anotherrefractive aspheric surface in its central region and adiscontinuous-slope structure in its external region, whosecross-section is formed of teeth with two aspheric faces such that onone of them, V, the bundle transmitted by surface S₃ is refracted sothat all the rays are reflected by total internal reflection on theother face, T, that the edge ray nearest to not being reflected istangent to the profile of the tooth, and that the face V is parallel tothe flow lines of the bundle transmitted toward S₁.
 28. Device accordingto claim 27 wherein at least one of said surfaces S₁, S₂, or S₃comprises a Cartesian oval.
 29. Device for concentrating radiant energywherein said device is axisymmetrical or cylindrical and is configuredto transform the edge rays of an input extended ray bundle into edgerays of an output extended ray bundle that illuminates a receiver, theoptical spread of at least one of said input and output bundles beinggreater than ten degrees at one or more of the optical surfaces of saiddevice and said bundles being defined in the plane of a cross-sectionby: a) a lens L₁ comprising on one side a refractive aspheric surface,S₁, on which the input bundle impinges, and on the other side, S₂,another refractive aspheric surface in its central region and adiscontinuous-slope structure in its external region, saiddiscontinuous-slope structure cross-section comprising teeth with twoaspheric faces such that one of them, V, is configured to be parallel tothe flow lines of the bundle transmitted by said surface S₁, and theother face, T, is configured to reflect the bundle by total internalreflection toward the face V where it is refracted so that no rayintercepts the adjacent tooth and that the nearest edge ray to do so istangent to that tooth, and b) A second lens L₂ that surrounds thereceiver composed of a refractive aspheric surface on which the bundletransmitted by the lens L₁ impinges.
 30. Device for collimating radiantenergy wherein said device is axisymmetrical or cylindrical and isconfigured to transform the edge rays of an input extended ray bundlegenerated by an emitter into edge rays of an output extended ray bundle,the optical spread of at least one of said input and output bundlesbeing greater than ten degrees at one or more of the optical surfaces ofsaid device, both of said bundles being defined in the plane of across-section, by: a) a lens L₂ that surrounds the emitter and comprisesa refractive aspheric surface S₃ on which the input bundle impinges, andb) a second lens L₁ comprising on one side a refractive asphericsurface, S₁, from which the output bundle leaves, and on the other side,S₂, another refractive aspheric surface in its central region and adiscontinuous-slope structure in its external region, saiddiscontinuous-slope structure cross-section comprising teeth with twoaspheric faces such that on one of them, V, the bundle transmitted bysaid surface S₃ is refracted so that all the rays are reflected by totalinternal reflection on the other face, T, that the edge ray nearest tonot being reflected is tangent to the profile of the tooth, and that theface V is parallel to the flow lines of the bundle transmitted towardS₁.